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We construct solutions in $\\mathbb{R}^3\\times [0,T]$ with a finite $T>0$ and with an external forcing which is in $L^1_t([0, T]) C_x^{1,\\epsilon}\\cap L^{\\infty}_{t}L_{x}^2$, such that on the time interval $0 \\le t < T$, the velocity $u$ is in the space $C^\\infty\\cap L^2$ and such that as the time $t$ approaches the b"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2407.06776","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-07-09T11:47:27Z","cross_cats_sorted":[],"title_canon_sha256":"8870f3bea9e7afd30e8f7fc5290eb2567b7fe1d1b1a68463ae56d1c71e564522","abstract_canon_sha256":"b3468c5dd27d98df91244fc299440b5ff7ed6b374f924bc8f04885ee1e0774bd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:51:54.454891Z","signature_b64":"UIlxTXoVFHiqPr7lnbaVbHpTmjki6SCiBNG64TkQIWATK139oL0uBDkZeb9+ghjKB+Qv2fo5IF1mX3TpBFlYBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"94ddaf221df1f4409027b19e06e790d89e54da5ad7710b2d7a5e0d9621b8ef62","last_reissued_at":"2026-07-05T08:51:54.454341Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:51:54.454341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finite time blow-up for the hypodissipative Navier Stokes equations with a force in $L^1_t C_x^{1,\\epsilon}\\cap L^{\\infty}_{t}L_{x}^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Diego C\\'ordoba, Fan Zheng, Luis Mart\\'inez-Zoroa","submitted_at":"2024-07-09T11:47:27Z","abstract_excerpt":"In this work we establish the formation of singularities of classical solutions with finite energy of the forced fractional Navier Stokes equations where the dissipative term is given by $|\\nabla|^{\\alpha}$ for any $\\alpha\\in [0, \\alpha_0)$ ($\\alpha_0 = \\frac{22-8\\sqrt7}{9} > 0$). 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